1. 9.3 Altitude-On-Hypotenuse Theorems Objective: After studying this section, you will be able to identify the relationships between the parts of a right triangle when an altitude is drawn to the hypotenuse

2. AB C D When altitude CD is drawn to the hypotenuse of triangle ABC, three similar triangles are formed. A B C D Therefore, AC is the mean proportional between AB and AD

3. A B C D Therefore, CB is the mean proportional between AB and DBTherefore, CD is the mean proportional between AD and DB C C A DDB

4. TheoremIf an altitude is drawn to the hypotenuse of a right triangle, then a. The two triangles formed are similar to the given right triangle and to each other. b. The altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse. h A B C D y b a x c

5. c. Either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg (i.e. the projection of that leg on the hypotenuse) h AB C D y a b x c

6. Example 1 If AD = 3 and DB = 9, find AC AB C D Example 2 If AD = 3 and DB = 9, find CD

7. If DB = 21 and AC = 10, find AD AB C D Example 3

8. Prove: (PO)(PM) = (PR)(PJ) JM P K Given: O R

9. Summary: Summarize what you learned from today’s lesson. Homework: Worksheet 9.3